title: Adjustment for regression dilution in epidemiological regression analyses.
abstract: OBJECTIVE
  The term "regression dilution" describes the dilution/attenuation in a regression coefficient that occurs when a single measured value of a covariate is used instead of the usual or average value over a period of time. This paper reviews the current knowledge concerning a simple method of adjusting for regression dilution in single and multiple covariate situations and illustrates the adjustment procedure.
  
  
  METHODS
  Formulation of the regression dilution problem as a measurement error problem allows existing measurement error theory to be applied to developing methods of adjustment for regression dilution. This theory leads to a precise method of adjustment for linear regression and approximate methods for logistic and Cox proportional hazards regression. The method involves obtaining the naive estimates of coefficients by assuming that covariates are not measured with error, and then adjusting these coefficients using reliability estimates for the covariates. Methods for estimating the reliability of covariates from the reliability and main study data and a method for the calculation of standard errors and confidence intervals for adjusted coefficients are described.
  
  
  RESULTS
  An illustration involving logistic regression analysis of risk factors for death from cardiovascular disease based on cohort and reliability data from the Busselton Health Study shows that the different methods for estimating the adjustment factors give very similar adjusted estimates of coefficients, that univariate adjustment procedures may lead to inappropriate adjustments in multiple covariate situations, whether or not other covariates have intra-individual variation, and when the reliability study is moderate to large, the precision of the estimates of reliability coefficients has little impact on the standard errors of adjusted regression coefficients.
  
  
  CONCLUSIONS
  The simple method of adjusting regression coefficients for "regression dilution" that arises out of measurement error theory is applicable to many epidemiological settings and is easily implemented. The choice of method to estimate the reliability coefficient has little impact on the results. The practice of applying univariate adjustments in multiple covariate situations is not recommended.
authors.affiliation: Department of Public Health, University of Western Australia, Nedlands, Australia.
authors.forename: M W
authors.initials: MW
authors.lastname: Knuiman
authors.forename: M L
authors.initials: ML
authors.lastname: Divitini
authors.forename: J S
authors.initials: JS
authors.lastname: Buzas
authors.forename: P E
authors.initials: PE
authors.lastname: Fitzgerald
mesh_terms: D000704:Analysis of Variance; D015982:Bias; D002318:Cardiovascular Diseases / Q000209:etiology / Q000401:mortality; D016001:Confidence Intervals; D003430:Cross-Sectional Studies; D003627:Data Interpretation, Statistical; D004812:Epidemiologic Methods; D006306:Health Surveys; D006801:Humans; D016014:Linear Models; D016015:Logistic Models; D008297:Male; D016016:Proportional Hazards Models; D015203:Reproducibility of Results; D012306:Risk; D012307:Risk Factors; D014904:Western Australia / Q000453:epidemiology